Today's knowledge of the parts of a pharmacokinetics and pharmacodynamic (PK/PD) system is increasingly detailed, and correspondingly complex models need to be devised for its description. The investigation of optimal experimental designs and the development of models which allow the incorporation of prior scientific knowledge and the integration of diverse pharmacological effects into a coherent picture of drug action is the main purpose of this grant proposal. Aim 1 investigates experimental design problems associated with PK/PD models. We will develop new methods for sample size calculations in population PK/PD studies. We will also investigate optimal sampling and optimal dosage regimen designs for PK/PD models when complete prior knowledge on the parts of a model is not available. We will develop algorithms to produce optimal designs for standard widely used PK/PD models, and investigate the performance of optimized designs in respect to empirical, frequently used ones. Aim 2 investigates specific applications of Bayesian analysis to complex physiologically based PK/PD models, concentrating on their performance in respect to semi empirical models, and their sensitivity to assumptions. We plan to develop and investigate the performance of novel Bayesian models for: (i) HIV-1 modeling in the presence of multi drug (HAART) therapy (incorporating virus phenotype, drug compliance and PK information), (ii) drug absorption using multi-site models and in-vivo/in vitro correlation, and (iii) in vitro/in vivo correlation of liposome distribution in anti-cancer therapy. Computer implementations of the models successfully developed will be provided. Aim 3 will provide a Bayesian framework for model-independent representations that do not require the sophistication of physiological models but retain the capability to incorporate prior knowledge. We will first investigate estimation methods incorporating prior knowledge for deconvolution in linear systems and develop Bayesian Marcov Chain Monte Carlo (MCMC) methods to obtain the desired estimates (an unknown absorption or input rate function) and their posterior distribution. Second, we will extend these MCMC methodologies to non-linear systems, providing improved algorithms for the estimation of Volterra representations, and developing a general method ("high order deconvolution") to estimate the input to a non linear system given its Volterra representation. Finally, we will develop a computer program for Bayesian linear and non-linear system analysis, which allows investigators to use the (model independent representations and MCMC-based methods we will investigate.